The Celtics shot just 25 per cent from the field and turned the ball over four times in the opening quarter before improving slightly in the second period to finish the half down by seven points.
During the break Boston point guard Kemba Walker told his team to "settle down a little bit", Jaylen Brown told reporters after the game, and the message penetrated as the Celtics erupted with 41 points in the third quarter.
Boston shot 50 per cent from the field in the second half, with forward Jayson Tatum collecting 17 points in the third quarter and finishing with 31 points as well as 10 rebounds by the time the clock stopped.
Miami had the chance to claim the Eastern Conference championship with a win, but they were simply not up to Boston's standard.
The Heat shot just seven-of-36 from three-point range and were constantly overwhelmed by the Celtics defence in the second half.
"We know what's at stake: We lose and go home," Tatum said in a post-game interview, with Boston now trailing 3-2 in the best-of-seven series.